Cayley is known for his 13 volumes of collected papers (with a 14th index volume), and his revisions of George Salmon's 'Higher Plane Curves'. As far as I know this is the only monograph he has actually written. It has more material on elliptic functions than you will probably ever need. It has unexpected things, like an expansion formula for the elliptic sine of 7 times an angle ( sn 7u ) in terms of the angle functions ( sn u, cn u and dn u). It has incredible change-of-base formulas for the elliptic parameter k. I know of no other book that goes into such meticulous computations with elliptic function and elliptic integrals. I reccomend it highly to anyone interested in elliptic functions or elliptic integrals. Being a product of the 19th century, it is missing one thing that moderns could desire: numeric algorithms for efficiently computing these functions. But these exist in modern literature for scientific computer programming. So read the book and get some software algorithms to compute whatever you need.